Sheffield Hallam MP, Jared O'Mara, was suspended by the Labour Party on Wednesday, while an investigation into a string of homophobic and misogynistic comments he is alleged to have posted online before becoming MP takes place.
Mr O'Mara, who unseated former Liberal Democrat leader, Nick Clegg, in June's General Election, has apologised for online remarks from 2002 and 2004 but denies some more recent claims.
Speaking on the Andrew Marr show this morning, Ms Abbott criticised comments made by Mr O'Mara.
"That language and that tone is not acceptable in 2017. We have now moved on and the leader of the Labour Party is very clear that we are going to be a party with zero tolerance for sexual harassment," said Ms Abbott.
When asked whether she believed Mr O'Mara could stay on as MP, she continued: "I can't judge because I've not seen the evidence.
"What I would say is that language and that tone is unacceptable. The party's moved on, and you know, where you have that sort of language and where you have that sort of harassment and sexual micro-aggression it demeans and diminishes all women that's why it's important to take a strong line."
Ms Abbott said she was not aware of the Labour Party being informed of Mr O'Mara's a month ago, as has been reported nationally.
She said: "I heard about it last Monday, he came to the PLP and apologised and people took his apology quite seriously but on Tuesday we had more information, and on Wednesday he was suspended. The Labour Party has looked at it, there's going to be an investigation."
Meanwhile the Liberal Democrats have brought forward their selection process to find a new candidate for Sheffield Hallam. It is understood there are five candidates, but Mr O’Mara’s predecessor, Nick Clegg, is not among them.
Mr O'Mara is also accused of calling a bar worker, Sophie Evans, an ‘ugly bitch’ on a night out in March this year. Mr O’Mara, 36, who has cerebral palsy and has campaigned on disability rights, resigned from the Women and Equalities select committee on Tuesday.
He issued an apology, saying he was ‘deeply ashamed’ and admitting the ‘offensive’ nature of his comments.
Labour admitted earlier this week that the party did not interview him before he was picked.